A method is proposed to computing a B-spline surface bounded by two fixed B-spline curves such that the surface achieves as large developability as possible. Existing methods generate discrete developable surfaces from line sequences connecting prespecified points sampled on input curves and need a highly dense sampling to achieve a high degree of developability which largely increases the problem complexity and computational time. Moreover, when generating smooth surfaces from the discrete lines, the parametrization of the sample points has a large impact on the developability of the interpolation surface. To overcome these drawbacks, we propose a variational method to compute a continuous mapping of input curves maximizing the developability of the surface defined by the mapping. The advantages of our method are twofold: by working with a continuous solution space rather than a restricted one composed of sample points, it can find mappings between input curves achieving the maximal developability; the resulting surface is directly a continuous surface and does not depend on any explicit data parametrization. The performance of the proposed method is analyzed from various aspects by experiments and method efficacy is demonstrated with several industrial examples.

提出了一种计算由两条固定的B样条曲线限制的B样条表面的方法，以使该表面获得尽可能大的可显影性。现有方法从连接输入曲线上采样的预定点的线序列生成离散的可显影表面，并且需要高度密集的采样以实现高度可开发性，这大大增加了问题的复杂性和计算时间。此外，当从离散线生成平滑表面时，采样点的参数化对插值表面的可显影性有很大影响。为了克服这些缺点，我们提出了一种变分方法来计算输入曲线的连续映射，以最大化由映射定义的表面的可开发性。我们方法的优点是双重的：通过使用连续的解空间而不是由样本点组成的受限解空间，它可以找到实现最大可开发性的输入曲线之间的映射。生成的表面直接是连续表面，并且不依赖于任何明确的数据参数化。通过实验从各个方面分析了所提出方法的性能，并通过几个工业实例证明了方法的有效性。